




'''simple docstring'''

from dataclasses import dataclass
from typing import Tuple

import numpy as np
import torch



@dataclass
class 		SCREAMING_SNAKE_CASE__  :
			__SCREAMING_SNAKE_CASE    =			42  # [batch_size x 3]
			__SCREAMING_SNAKE_CASE    =			42  # [batch_size x 3]
			__SCREAMING_SNAKE_CASE    =			42  # [batch_size x 3]
			__SCREAMING_SNAKE_CASE    =			42  # [batch_size x 3]
			__SCREAMING_SNAKE_CASE    =			42
			__SCREAMING_SNAKE_CASE    =			42
			__SCREAMING_SNAKE_CASE    =			42
			__SCREAMING_SNAKE_CASE    =			42
			__SCREAMING_SNAKE_CASE    =			42





			def 							A (      self						:    List[str]							):



						"""simple docstring"""




						assert self.x.shape[0] == self.y.shape[0] == self.z.shape[0] == self.origin.shape[0]
						assert self.x.shape[1] == self.y.shape[1] == self.z.shape[1] == self.origin.shape[1] == 3
						assert len(self.x.shape							) == len(self.y.shape							) == len(self.z.shape							) == len(self.origin.shape							) == 2





			def 							A (      self						:    Dict							):



						"""simple docstring"""




						return torch.from_numpy(np.array([self.width, self.height]      ,		dtype=np.floataa							)							)





			def 							A (      self						:    Optional[Any]							):



						"""simple docstring"""




						return torch.from_numpy(np.array([self.x_fov, self.y_fov]      ,		dtype=np.floataa							)							)





			def 							A (      self						:    Optional[int]							):



						"""simple docstring"""




						__snake_case			=		torch.arange(self.height * self.width							)
						__snake_case			=		torch.stack(
						    [
						        pixel_indices % self.width,
						        torch.div(a_      ,		self.width      ,		rounding_mode="trunc"							),
						    ]      ,		axis=1      ,		)
						return coords





			@property
			def 							A (      self						:    Optional[int]							):



						"""simple docstring"""




						__snake_case		,     *__snake_case			=		self.shape
						__snake_case			=		int(np.prod(a_							)							)

						__snake_case			=		self.get_image_coords()
						__snake_case			=		torch.broadcast_to(coords.unsqueeze(0							)      ,		[batch_size * inner_batch_size, *coords.shape]							)
						__snake_case			=		self.get_camera_rays(a_							)

						__snake_case			=		rays.view(a_      ,		inner_batch_size * self.height * self.width      ,		2      ,		3							)

						return rays





			def 							A (      self						:    Optional[int]      ,		a_						:    torch.Tensor							):



						"""simple docstring"""




						__snake_case		,     *__snake_case		,     __snake_case			=		coords.shape
						assert n_coords == 2
						assert batch_size == self.origin.shape[0]

						__snake_case			=		coords.view(a_      ,		-1      ,		2							)

						__snake_case			=		self.resolution()
						__snake_case			=		self.fov()

						__snake_case			=		(flat.float() / (res - 1)) * 2 - 1
						__snake_case			=		fracs * torch.tan(fov / 2							)

						__snake_case			=		fracs.view(a_      ,		-1      ,		2							)
						__snake_case			=		(
						    self.z.view(a_      ,		1      ,		3							)
						    + self.x.view(a_      ,		1      ,		3							) * fracs[:, :, :1]
						    + self.y.view(a_      ,		1      ,		3							) * fracs[:, :, 1:]
						)
						__snake_case			=		directions / directions.norm(dim=-1      ,		keepdim=a_							)
						__snake_case			=		torch.stack(
						    [
						        torch.broadcast_to(self.origin.view(a_      ,		1      ,		3							)      ,		[batch_size, directions.shape[1], 3]							),
						        directions,
						    ]      ,		dim=2      ,		)
						return rays.view(a_      ,		*a_      ,		2      ,		3							)






			def 							A (      self						:    List[str]      ,		a_						:    int      ,		a_						:    int							):



						"""simple docstring"""




						assert width * self.height == height * self.width, "The aspect ratio should not change."
						return DifferentiableProjectiveCamera(
						    origin=self.origin      ,		x=self.x      ,		y=self.y      ,		z=self.z      ,		width=a_      ,		height=a_      ,		x_fov=self.x_fov      ,		y_fov=self.y_fov      ,		)







def __UpperCAmelCase	(   _UpperCAmelCase		:   int						)      ->      DifferentiableProjectiveCamera:
			__snake_case			=		[]
			__snake_case			=		[]
			__snake_case			=		[]
			__snake_case			=		[]
			for theta in np.linspace(0		,				2 * np.pi		,				num=20						):
						__snake_case			=		np.array([np.sin(_UpperCAmelCase						), np.cos(_UpperCAmelCase						), -0.5]						)
						z /= np.sqrt(np.sum(z**2						)						)
						__snake_case			=		-z * 4
						__snake_case			=		np.array([np.cos(_UpperCAmelCase						), -np.sin(_UpperCAmelCase						), 0.0]						)
						__snake_case			=		np.cross(_UpperCAmelCase		,				_UpperCAmelCase						)
						origins.append(_UpperCAmelCase						)
						xs.append(_UpperCAmelCase						)
						ys.append(_UpperCAmelCase						)
						zs.append(_UpperCAmelCase						)
			return DifferentiableProjectiveCamera(
			    origin=torch.from_numpy(np.stack(_UpperCAmelCase		,				axis=0						)						).float()		,				x=torch.from_numpy(np.stack(_UpperCAmelCase		,				axis=0						)						).float()		,				y=torch.from_numpy(np.stack(_UpperCAmelCase		,				axis=0						)						).float()		,				z=torch.from_numpy(np.stack(_UpperCAmelCase		,				axis=0						)						).float()		,				width=_UpperCAmelCase		,				height=_UpperCAmelCase		,				x_fov=0.7		,				y_fov=0.7		,				shape=(1, len(_UpperCAmelCase						))		,				)








import string
from math import logaa






def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_		):
							A      :					List[str]      		=					document.translate(
							    str.maketrans(''''''     ,				''''''     ,				string.punctuation		)		).replace('''\n'''     ,				''''''		)
							A      :					Optional[int]      		=					document_without_punctuation.split(''' '''		)  # word tokenization
							return len([word for word in tokenize_document if word.lower() == term.lower()]		)






def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_		):
							A      :					Dict      		=					corpus.lower().translate(
							    str.maketrans(''''''     ,				''''''     ,				string.punctuation		)		)  # strip all punctuation and replace it with ''
							A      :					Dict      		=					corpus_without_punctuation.split('''\n'''		)
							A      :					List[Any]      		=					term.lower()
							return (len([doc for doc in docs if term in doc]		), len(lowerCamelCase_		))






def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_     ,				lowerCamelCase_=False		):
							if smoothing:
														if n == 0:
																					raise ValueError('''log10(0) is undefined.'''		)
														return round(1 + logaa(n / (1 + df)		)     ,				3		)

							if df == 0:
														raise ZeroDivisionError('''df must be > 0'''		)
							elif n == 0:
														raise ValueError('''log10(0) is undefined.'''		)
							return round(logaa(n / df		)     ,				3		)






def        snake_case__		(    lowerCamelCase_     ,				lowerCamelCase_		):
							return round(tf * idf     ,				3		)






